Question:

The net reaction of the disc on the block is:

mω²Rsinωt^j−mg^k

12mω²R(eωt−e⁻ωt)^j+mg^k

12mω²R(e²ωt−e⁻²ωt)^j+mg^k

−mω²Rcosωt^j−mg^k

Solution:

Frot=Fin+2m(vrot^i)×ω^k+m(ω^k×r^i)×ω^kmrω²^i=Fin+2mvrotω(−^j)+mrω²^iFin=2mvrotω^jr=R4(eωt+e⁻ωt)vr=drdt=Rω4(eωt−e⁻ωt)Fin=2mω²R4(eωt−e⁻ωt)^jFreaction=mω²R2(eωt−e⁻ωt)^j+mg^k